As the Columbus City Council begins 2012 budget hearings this week, members have about $800,000 to work with if they stick to Mayor Michael B. Coleman's proposals.

That number is likely to grow before the end of the year, leaving more for council priorities such as helping the homeless, reopening more swimming pools and offering free graffiti removal to homes and businesses.

"My belief is that it will change," said Paul Rakosky, Coleman's finance director. "Some revenues are coming in better than (Auditor Hugh Dorrian's) revised projections. And we usually save more than we project in our third-quarter review."

Coleman proposed a $735.5 million budget on Nov. 15. But Dorrian predicted, based on city finances through September, that nearly $736.3 million in revenue would be available to operate the city in 2012, meaning that right now there's about $800,000 the mayor didn't allocate.

More money for the council's priorities would have to come from a better-than-predicted carryover at the end of the year or from cuts to Coleman's proposals.

Last year, the council added no spending to the mayor's 2011 budget proposal and asked Coleman to trim his plan in anticipation of state budget cuts to cities. Together, they left $3million unappropriated.

This year, Coleman's budget already sets aside $10 million against state cuts for 2013.

"We can make amendments this year," said Councilwoman Priscilla R. Tyson, who leads the council's finance committee.

Even before hearings have begun, council members have heard from social-service agencies that are seeing more people in need, Tyson said. They've also heard from residents concerned about reopening city pools, some of which have been closed since a 2009 budget crunch.

It cost about $120,000 to open two closed pools - Maryland Pool on the Near East Side and Glenwood Pool on the Hilltop - this summer, and both opened later in the season. Coleman's budget proposal did not include money to reopen those pools this year, funding only the four that were open the entire 2011 season.

"I'm looking forward to having a robust conversation about the carryover and figuring out what we can do with Recreation and Parks, including the pools," said Councilman Zach M. Klein. He proposed reopening the two pools last summer using hotel tax money left over from another program.

Klein said his priorities this year also include help for small businesses and a graffiti-removal program he proposed with Councilwoman Michelle M. Mills this fall that's estimated to cost $800,000 to $2.4 million per year. It would serve a dual purpose of making neighborhoods more attractive for development and less attractive to criminals, Klein said.

But any decision will take into account the money available.

"We're going to balance the budget priorities and being fiscally prudent," Klein said.

Dorrian said that he is sticking with his revenue estimates, but he expects to revise them well before the council votes on the budget in early February. If there's more money available, he said, he's encouraging the council to help the Community Shelter Board, which is seeing a steep increase in homeless families.

In late 2010, then-council President Michael C. Mentel championed spending an extra $300,000 to help the board. That amount might not be possible, Tyson said, but the homeless are certainly on the council's radar.